**Title:** Using Exploration and Discovery To Determine the Vertices of Transformed Images

**Description:**
This hands-on lesson uses exploration and discovery to help students determine the coordinates of the vertices of various figures when translated, rotated, or reflected in a coordinate plane. The exploration phase will access students' prior knowledge and prepare them for the assigned task of using and applying their understanding of transformed images to new situations. The final project will be a cooperative activity, requiring collaboration in the application phase to discover the patterns and create graphs following directions unique to each group.
**Standard(s): **

[MA2015] (8) 18: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. [8-G3]

**Subject:**Mathematics (8)

**Title:**Using Exploration and Discovery To Determine the Vertices of Transformed Images

**Description:**This hands-on lesson uses exploration and discovery to help students determine the coordinates of the vertices of various figures when translated, rotated, or reflected in a coordinate plane. The exploration phase will access students' prior knowledge and prepare them for the assigned task of using and applying their understanding of transformed images to new situations. The final project will be a cooperative activity, requiring collaboration in the application phase to discover the patterns and create graphs following directions unique to each group.

**Title:** Geometric Quilts

**Description:**
Students will use a square to investigate other polygonal shapes that can be formed. Students will work with these polygons to make designs that will later constitute cooperatively designed quilts. The quilts will be made by translating, rotating, or reflecting a thirty-six patch design. The completed quilts will then be used for a discussion of area and perimeter. Students will blog about what they have learned while doing the lesson and will include pictures of their finished product in our class blog.
**Standard(s): **

[MA2015] GEO (9-12) 34: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama)

**Subject:**Mathematics (8 - 12)

**Title:**Geometric Quilts

**Description:**Students will use a square to investigate other polygonal shapes that can be formed. Students will work with these polygons to make designs that will later constitute cooperatively designed quilts. The quilts will be made by translating, rotating, or reflecting a thirty-six patch design. The completed quilts will then be used for a discussion of area and perimeter. Students will blog about what they have learned while doing the lesson and will include pictures of their finished product in our class blog.

**Title:** Relationships Between Reflections and Symmetry

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students learn the properties of designs that have bilateral symmetry. They also make their own designs and investigate dihedral symmetry.
**Standard(s): **

[MA2015] (8) 19: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. [8-G4]

**Subject:**Mathematics

**Title:**Relationships Between Reflections and Symmetry

**Description:**In this lesson, one of a multi-part unit from Illuminations, students learn the properties of designs that have bilateral symmetry. They also make their own designs and investigate dihedral symmetry.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Symmetries I

**Description:**
In this unit of four lessons, from Illuminations, investigate rotational symmetry. They learn about the mathematical properties of rotations and have an opportunity to make their own designs.
**Standard(s): **

[MA2015] GEO (9-12) 14: Verify experimentally the properties of dilations given by a center and a scale factor. [G-SRT1]

**Subject:**Mathematics

**Title:**Symmetries I

**Description:**In this unit of four lessons, from Illuminations, investigate rotational symmetry. They learn about the mathematical properties of rotations and have an opportunity to make their own designs.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Symmetries II

**Description:**
In this unit of four lessons, from Illuminations, students use Java applets to investigate reflection, mirror, or bilateral symmetry. They learn about the mathematical properties of mirror symmetry and have a chance to create designs with mirror symmetry.
**Standard(s): **

[MA2015] GEO (9-12) 16: Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. [G-SRT3]

**Subject:**Mathematics

**Title:**Symmetries II

**Description:**In this unit of four lessons, from Illuminations, students use Java applets to investigate reflection, mirror, or bilateral symmetry. They learn about the mathematical properties of mirror symmetry and have a chance to create designs with mirror symmetry.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Go the Distance

**Description:**
This lesson is the fourth part of a four-part Illuminations unit titled '' Analyzing Numeric and Geometric Patterns of Paper Pool.'' The interactive paper pool game in this unit provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. At the end of the lesson, students write reports on their findings. This resource is referenced in the Illuminations unit titled '' Analyzing Numeric and Geometric Patterns of Paper Pool'' and is related to the Illuminations lessons titled '' Paper Pool Game,'' '' Explore More Tables,'' '' Look for Patterns.''
**Standard(s): **

[MA2015] (8) 18: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. [8-G3]

**Subject:**Language Arts,Mathematics

**Title:**Go the Distance

**Description:**This lesson is the fourth part of a four-part Illuminations unit titled '' Analyzing Numeric and Geometric Patterns of Paper Pool.'' The interactive paper pool game in this unit provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. At the end of the lesson, students write reports on their findings. This resource is referenced in the Illuminations unit titled '' Analyzing Numeric and Geometric Patterns of Paper Pool'' and is related to the Illuminations lessons titled '' Paper Pool Game,'' '' Explore More Tables,'' '' Look for Patterns.''

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Algebraic Transformations

**Description:**
In this unit of two lessons, from Illuminations, students learn about the commutative and associative properties using geometric shapes. They investigate the concepts first using a rectangle then using a plus sign shape and a triangle.
**Standard(s): **

[MA2015] (8) 18: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. [8-G3]

**Subject:**Mathematics

**Title:**Algebraic Transformations

**Description:**In this unit of two lessons, from Illuminations, students learn about the commutative and associative properties using geometric shapes. They investigate the concepts first using a rectangle then using a plus sign shape and a triangle.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Commutative Rectangle

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students investigate the concepts of identity, inverse, commutativity, and associativity using a geometric model. Moves are performed with a rectangle, and the results of an operation that combines two moves are analyzed. Students determine if the operation is commutative or associative, if an identity element exists, or if there are inverses for any of the moves.
**Standard(s): **

[MA2015] (8) 18: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. [8-G3]

**Subject:**Mathematics

**Title:**Commutative Rectangle

**Description:**In this lesson, one of a multi-part unit from Illuminations, students investigate the concepts of identity, inverse, commutativity, and associativity using a geometric model. Moves are performed with a rectangle, and the results of an operation that combines two moves are analyzed. Students determine if the operation is commutative or associative, if an identity element exists, or if there are inverses for any of the moves.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Visualizing Transformations

**Description:**
The interactive figures in this four-part example from Illuminations allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
**Standard(s): **

[MA2015] GEO (9-12) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. *Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.* [G-CO12]

**Subject:**Mathematics

**Title:**Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Visualizing Transformations

**Description:**The interactive figures in this four-part example from Illuminations allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Identifying Unknown Transformations

**Description:**
**Standard(s): **

[MA2015] GEO (9-12) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. *Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.* [G-CO12]

**Subject:**Mathematics

**Title:**Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Identifying Unknown Transformations

**Description:**

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Reflections

**Description:**
This is part three of a four-part e-example from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Reflections, users can examine the result of reflecting a shape successively through two different lines. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.
**Standard(s): **

[MA2015] GEO (9-12) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. *Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.* [G-CO12]

**Subject:**Mathematics

**Title:**Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Reflections

**Description:**This is part three of a four-part e-example from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Reflections, users can examine the result of reflecting a shape successively through two different lines. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Transformations

**Description:**
This is part four of a four-part e-example from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Transformations, the users are challenged to compose equivalent transformations in two different ways. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.
**Standard(s): **

[MA2015] GEO (9-12) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software.

**Subject:**Mathematics

**Title:**Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Transformations

**Description:**This is part four of a four-part e-example from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Transformations, the users are challenged to compose equivalent transformations in two different ways. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Calculation Nation

**Description:**
Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement.
**Standard(s): **

[MA2015] DM1 (9-12) 1: Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine properties of integers. (Alabama)

**Subject:**Mathematics

**Title:**Calculation Nation

**Description:**Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8,9